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About LinkBackscalculate all polynomialfor which
)^2+(p(x-1))^2+1=(P(x)-x)^2)
If you put x=0 in this equation then you getOriginally Posted by jacks
calculate all polynomial. This cannot happen if the polynomial has real coefficients. So there are no such real polynomials. If complex coefficients are allowed, then
, but I don't see where to go from there.
If we presume that p(x) is going to have at least real coefficients we can expland the definig equation to getcalculate all polynomial
The above says that p(x) must contain a factor of x + 1 and since no real p(0) exists (ala Opalg) we must also require that p(x) contains a factor of x as well, so we have
where q(x) is a polynomial. This expression needs to be run through the original equation to get restrictions on q(x), but I can't make any sense out of the resulting equation.
-Dan
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